Introduction and books 1,2The University Press, 1908 |
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Side 7
... take first the works which are mentioned by Greek authors . 1. The Pseudaria . I mention this first because Proclus refers to it in the general remarks in praise of the Elements which he gives immediately after the mention of Euclid in ...
... take first the works which are mentioned by Greek authors . 1. The Pseudaria . I mention this first because Proclus refers to it in the general remarks in praise of the Elements which he gives immediately after the mention of Euclid in ...
Side 9
... take one more example : " To cut off a certain fraction from a ( parallel- ) trapezium by a straight line which passes through a given point lying inside or outside the trapezium but so that a straight line can be drawn through it ...
... take one more example : " To cut off a certain fraction from a ( parallel- ) trapezium by a straight line which passes through a given point lying inside or outside the trapezium but so that a straight line can be drawn through it ...
Side 11
... take Prop . 5 as an example , DBF is a tangent to a circle with centre K. It is then possible , says Archimedes , to draw a straight line KHF , meeting the circumference in H and the tangent in F , such that FH : HK < ( arc BH ) : c ...
... take Prop . 5 as an example , DBF is a tangent to a circle with centre K. It is then possible , says Archimedes , to draw a straight line KHF , meeting the circumference in H and the tangent in F , such that FH : HK < ( arc BH ) : c ...
Side 21
... takes a wrong point to be the fulcrum ; and it is held that he cannot have made the mistake himself , but must necessarily have copied it from Heron . In order , however , to find the same error in Heron , Hoppe arbitrarily alters both ...
... takes a wrong point to be the fulcrum ; and it is held that he cannot have made the mistake himself , but must necessarily have copied it from Heron . In order , however , to find the same error in Heron , Hoppe arbitrarily alters both ...
Side 24
... takes this book to have been a work by Porphyry mentioned by Suidas and Proclus ( Theolog . Platon . ) , περὶ ἀρχῶν libri II . There is nothing of importance in the notes attributed to Porphyry by Proclus . ( 1 ) Three alternative ...
... takes this book to have been a work by Porphyry mentioned by Suidas and Proclus ( Theolog . Platon . ) , περὶ ἀρχῶν libri II . There is nothing of importance in the notes attributed to Porphyry by Proclus . ( 1 ) Three alternative ...
Vanlige uttrykk og setninger
angle ABC angle ACB angle BAC angles equal Apastamba Apollonius Arabic Archimedes Aristotle assumed axiom base BC bisects Book Campanus centre circle circumference coincide commentary Common Notion congruent construction contained definition diameter drawn edition Elements enunciation equal angles equal sides equal to AC Eucl Euclid Euclid's Elements Eudemus Eutocius exterior angle figure Fihrist follows Geminus geometry given straight line gives gnomon greater Greek Heiberg Heron hypothesis ibid interpolated isosceles triangle joined lemma length less Let ABC magnitude means meet method observed Pappus parallel parallelogram passage perpendicular plane Plato porism Posidonius postulate problem Proclus produced proposition proved Pythagoras Pythagorean Pythagorean theorem quoted rectangle reductio ad absurdum reference remaining angles respectively right angles right-angled triangle says Schol scholia segment semicircle Simplicius Simson square suppose surface Theon Theonine MSS theorem things translation triangle ABC words καὶ τὸ
Populære avsnitt
Side 322 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Side 204 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Side 259 - If two triangles have two sides of the one equal to two sides of the...
Side 188 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Side 204 - In any triangle, the sum of the three angles is equal to two right angles, or 180°.
Side 162 - A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line.
Side 167 - When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.
Side 257 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Side 176 - Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.
Side 235 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of' the base, equal to one another, and likewise those which are terminated in the other extremity.